Electrons in Atoms script
Introduction
In this activity you are going to explore the quantum world of the atom.
This is a world of energy levels, of emission and absorption spectra, and of electron clouds associated with quantum states. All of these aspects of quantum physics are intimately related, and you're going to explore these relationships. You'll manipulate atoms - causing them to make transitions from one quantum state to another - and you'll investigate the emission and absorption lines in their spectra, and changes in the electron cloud pictures.
Your exploration will be limited to three atoms - hydrogen with atomic number Z of 1, helium with atomic number 2, and lithium with atomic number 3. You'll start with hydrogen, which has a single positively charged proton and a single negatively charged electron - this is the simplest possible atom. The helium atom has two protons and two neutrons in the nucleus, and there are two electrons around it that balance the charge. But you'll be looking at the 'He+' ion, which has just a single electron. You'll investigate how the energy levels and the spectra of this ion differ from those of the H atom (shown in the top row), and you'll formulate hypotheses for how these differences depend on the atomic number Z. Then you'll test out your hypotheses on the 'Li2+' ion, which again has a single electron, but this time has three protons in the nucleus.
Click on the forward arrow when you are ready to move on to the second part of the introduction.
Introduction to Tools
(Energy levels tool)
You've got three 'tools' here to use in your investigation.
On the left, there's an energy level diagram, and this displays the seven lowest energy levels of the atom, or ion, you're exploring. You can use the scroll bar to move down through the energy range or up, as far as zero electron volts and you can use the arrows on the scale control to compress the energy scale or to enlarge it. When you move the pointer over the energy level diagram the arrow turns into a gray disc, and when this disc is positioned over an energy level, it turns white and the value of the energy is displayed; if you click when the energy value is displayed, you force the atom to be in that particular level, and this is indicated by the blue disc. Then, if you move the pointer to another level, and you click there, you force the atom to make a transition, indicated by the arrow, to the new level, and the energy 'change', 1.89 eV in this case, is displayed at the bottom of the diagram.
(Spectrum tool)
Your second tool, up at the top, is the spectra panel. At the moment, this is showing an 'emission' spectrum - bright lines on a dark background - but clicking on the absorption button changes it to an 'absorption' spectrum. The visible spectrum is shown coloured, and the infrared region - the low energy region below the red - and the ultraviolet region - the high energy region beyond the violet - are both shown in grey. Scrolling through the spectrum is done in the same way as for the energy levels, except this time the display scrolls in the horizontal direction and clicking on the arrows on the scale control compresses the energy scale or expands it. When the pointer is positioned over a line in the spectrum, the energy of the photons associated with that line is displayed.
(Electron cloud tool)
The third tool, at the bottom right, is the electron cloud display. This shows a cloud picture for one of the quantum states for the energy level that the atom, or ion, is occupying - n = 3 at the moment. The scale control allows you to compress the cloud or to magnify it, and the easiest way to get a rough measure of the size of a feature is to adjust the scale control until the feature roughly fills the window and then to note the length on the scale bar.
Quantum jumps in the hydrogen atom - Introduction
In this section, you're going to investigate the links between the energy levels, the spectra, and the electron clouds of hydrogen atoms. You'll start by thinking about how the transitions between levels are linked to absorption and emission of photons and you'll then identify the lines in the hydrogen spectrum that are associated with various transitions. Finally you'll look at some of the electron clouds associated with quantum states for the different levels.
Quantum jumps in the hydrogen atom – Summary
This investigation of the hydrogen atom should have reinforced some basic concepts of quantum physics. Atoms can only have certain energies - their energy levels - and when they make transitions between these energy levels they either emit photons, or they absorb photons. The photon energies correspond precisely to the energy differences between the levels, which is why atoms have line spectra. The different quantum states for the different energy levels can be represented by electron cloud pictures, with the clouds becoming more spread out as the quantum number n increases.
Now we've introduced these quantum physics concepts by investigating the hydrogen atom, but they are equally valid for other atoms and ions, as you'll discover in the following sections.
The Helium ion - Introduction
Helium atoms have atomic number two, which means that they have two protons in the nucleus, and they have two electrons to balance the charge of the protons. If one of the electrons is removed, the result is a 'He+' ion. This ion has a single electron, just like the hydrogen atom, but it has a more massive nucleus, and its nucleus has double the charge on a hydrogen nucleus.
But what is the effect of increasing the charge on the nucleus? That is the question that you'll be trying to answer in this section. Your objective is to discover how the change from hydrogen atom to helium ion - a change from a nucleus with Z = 1 to Z = 2 - affects the energy levels, the spectra and the electron clouds.
The Helium ion - Summary
The evidence from comparing the He+ ion and the H atom has led to the hypotheses that energy levels and photon energies are proportional to Z squared, and that the sizes of the electron clouds are proportional to 1/Z.
But these hypotheses are based on very limited evidence - from just two values of Z! In the final section you'll test these hypotheses by investigating the hydrogen-like ion that has Z = 3.
The Lithium ion - Introduction
In this final section you'll investigate briefly the Li2+ ion. Lithium, with atomic number Z = 3, has three protons in the nucleus, and there are three electrons in a neutral atom. Remove two of the electrons and you get a Li2+ ion. There is just a single electron bound to this nucleus - so it's another hydrogen-like ion.
Your objective is to test the hypotheses that energy levels and spectra for hydrogen-like ions are proportional to Z squared, and that the sizes of the electron clouds are proportional to 1/Z.
The Lithium ion - Summary
So your investigation of the energy levels, the spectra and the electron clouds of Li2+ has confirmed the hypotheses arrived at by studying H and He+:
- the energy levels are proportional to Z squared
- the photon energies in the spectra are also proportional to Z squared
- and the overall size of the electron clouds are proportional to 1/Z
Conclusions
You have discovered that the energy levels, the emission and absorption spectra and the electron clouds for the hydrogen atom, the He+ ion and the Li2+ ion depend on atomic number Z, and the same dependence of the quantum properties on Z holds for all single-electron ions, such as Be3+, B4+, C5+, and so on. This is because the electrical force between an electron and a nucleus is proportional to the charge on the nucleus, and therefore to the atomic number Z. The larger the value of Z, the larger this electrical force, and so the more closely the electron is bound to the nucleus and the smaller the size of the electron cloud. Also the increase in the electrical force with increasing Z means that the energy of a given level increases with Z. So, larger atomic number Z means wider spacing between the energy levels, and greater energies for the photons that are emitted and absorbed.
We've only looked at atoms and ions with a single electron - the spectra and electron clouds for atoms with more than one electron are much more complicated. But however complex an atom or ion, the basic relationship between energy levels and spectra is exactly the same - transitions between energy levels lead to emission or absorption of photons, and the energies of those photons are exactly equal to the differences between the energy levels.